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					      JOURNAL DE PHYSIQUE                                                  Colloque C6, suppl6ment au no 8, Tome 39, aolit 1978, page                       C6-3 16




          SURFACE DEFORMATION AND SURFACE MOTION DUE T O STANDING SECOND SOUND WAVES
            IN HELIUM I 1

                       S.G. Eckstein*,           Y. Eckstein*,          J.L.    Olsen and H. Sigg

                       Laboratoriwn ftir Festk8rperphysik, Swiss Federal I n s t i t u t e of Technology,
                                                   r
                       8093 Ziirich, ~ z J i t i eland


                       R6sum6.-      On a observg l a dgformation d'une s u r f a c e l i b r e d'hdlium l i q u i d e en prgsence
                       d'ondes s t a t i o n n a i r e s d e second son. L'amplitude mesurge e s t 10 P 100 f o i s i n f g r i e u r e
                       B c e l l e correspondant 5 l a p r e s s i o n associde au second son l o i n de l a s u r f a c e . La db-
                       pendance temporelle de l a s u r f a c e e s t nggligeable.

                       Abstract.- The amplitude of the deformation of t h e f r e e s u r f a c e of l i q u i d helium i n
                       t h e presence of s t a n d i n g waves of second sound h a s been observed. The wave h e i g h t i s 10-
                       100 times smaller t h a n t h a t corresponding t o t h e second sound p r e s s u r e away from t h e
                       s u r f a c e . The time dependence of t h e s u r f a c e l e v e l i s v a n i s h i n g l y small.



                       I t h a s been pointed o u t elsewhere t h a t                       v a r i a t i o n of z i s l i m i t e d by i n e r t i a l e f f e c t s
        s t a n d i n g waves of second sound i n He I1 produce de-                         s i n c e t h e r e w i l l be bulk flow i f Az i s t o follow
        formations of t h e f r e e s u r f a c e , and t h a t t h e s e can               p2 a t t h e frequency 2w.
        be observed u s i n g o p t i c a l techniques / 1 , 2 / .                                      A simple c a l c u l a t i o n shows t h a t t h e ampli-;
                       The second sound f i e l d c o n t r i b u t e s t o t h e           tude A of t h e o s c i l l a t i o n o f t h e s u r f a c e h e i g h t i s
        p r e s s u r e w i t h i n t h e l i q u i d , and theamount of t h i s            reduced t o
        p r e s s u r e has been c a l c u l a t e d by v a r i o u s a u t h o r s                           v 2
                                                                                            A = -P2            g
        /3,4,5/.      There i s l i t t l e doubt about t h e amplitude                            pg     (vg2+vc2-v22)
        of t h i s p r e s s u r e v a r i a t i o n f o r a given v a l u e of
        t h e second sound f i e l d . There remain, however, theo-                         Where v     and v a r e t h e v e l o c i t i e s of g r a v i t y wa-
                                                                                                     g
        r e t i c a l and experimental u n c e r t a i n t i e s about both                 v e s and c a p i l l a r y waves a t frequency 20, and vt i s
        t h e time average and t h e time dependence of t h e                               t h e v e l o c i t y of second sound. For wavelengths of
        r e s u l t i n g s u r f a c e deformation.                                        a few m i l l i m e t e r s a s used i n our experiments, A
                      The problems a r i s i n g a r e most e a s i l y seen                w i l l be approximately                   times Az a s         given by
        i f we consider s t a n d i n g waves of second sound                               (3).
        given by                                                                                        The s u r f a c e motion i s c l e a r l y very small.
        $ = Qo s i n kx. cos w t ,                                                 (1)      On t h e o t h e r hand t h e time           average of p2 i s non-
        where$:       -   Vv-n i s t h e v e l o c i t y p o t e n t i a l of t h e         zero so t h a t we expect some kind of s u r f a c e de-
        normal f l u i d . The p r e s s u r e c o n t r i b u t i o n p2 r e s u l -       formation. Indeed we do observe c l e a r l y defined
        t i n g can be found u s i n g an expression given by                               s u r f a c e deformations /1,2/.           Close bo t h e s u r f a c e
        Sorbello /4/ which according t o P u t t e m a n and                                v      and v - ~     must be p a r a l l e l t o t h e s u r f a c e and
                                                                                             -n
        G a r r e t t / 5 / i s v a l i d i f c o m p r e s s i b i l i t y and ther-       c o n t a i n v e r t i c a l components. The p o t e n t i a l ( 9 )
       n a l expansion o f t h e l i q u i d a r e neglected.                               must t h e r e f o r e c l e a r l y be changed c l o s e t o t h e
               Ppn
       P2 = -       k2 $02 c o s 2kx(l - cos 2wt)             (2)                           s u r f a c e . This w i l l lead t o a c e r t a i n r e d u c t i o n i n
               2psIti s tempting t o conclude t h a t t h e sur-                            t h e time average below t h a t expected from
        f a c e w i l l be d i s p l a c e d from i t s e q u i l i b r i u m h e i g h t   < Az > = < p p >        1   p g                                             (5)
       by                                                                                                e
                                                                                                        W used t h e s c h l i e r e n technique described
           Az = pplpg.                                                             (3)      previously / I /       t o observe s u r f a c e deformations on
                      It t u r n s o u t , however, t h a t t h e time                      helium contained i n a v e r t i c a l c y l i n d e r e x c i t e d
                                                                                            thermally on t h e a x i s . The a c t u a l shape of t h e s e
      * At t h e Technion Haifa, I s r a e l . T h i s work was car-
                                                                                                                         be                 seen and photogra-
       ried out w h i l e s. and Y. Eckstein were on leave         of
       absence a t t h e Swiss Federal I n s t i t u t e o f Techno-                        phed. I n f i r s t approximation t h e resonances
       logy.




Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786140
correspond to those calculated by Rayleigh for
                                                                         References
aerial vibrations in a cylindrical symmetry. The
resonance frequencies suggest a Q value for the
                                                       /I/ Olsen, J.L. Physica 69 (1973) 803
cavity of the order of 5 x   lo2.   Some 80 separate
                                                       / 2 / Mota, A.C., Olsen, J.L. Sorbello, R.S., and
resonance frequencies could be observed and identi-        Tomar, V.S., Phys. Letters 46 (1974) 343.
fied with Rayleigh solutions.                          / 3 / Lukosz, W., 3. Low Temp. Phys. l(1969)   407.
         In our experimental arrangement the tempe-    /4/ Sorbello, R.S., J. Low Temp. Phys.   12 (1976)
rature excursions in the liquid could not be mea-          411.

sured directly. They may, however, be calculated       /5/ Putterman, S., and Garrett, J., J. Low Temp.
                                                                  7
                                                           Phys. 2 (1977) 543.
from the heater input if the heat transfer coef-
                                                       /6/ Eckstein, S., Eckstein, Y. and Olsen, J.L.Helv.
ficients at heater surface and at the outer boun-          Phys. Acta, 50 (1977) 6'
dary of the resonator are known. We have shown
elsewhere 161 that these can be calculated from
the deviation of the observed resonance frequen-
cies from the Rayleigh values.
         We have used such information to calculate
the second sound field in our resonators and to
calculate the value of pp away from the surface.
In the case of a cavity of 1 cm radius heated at
a frequency of 3000-5000 Hz with an r.m.s power
of 60 mW per cm of heater, the value of pp would
lead to wave heights of approximately 0.5 mm at a
distance 0.5 cm from the axis if the expression
(5) is used.
         New careful experimental observations of
the wave height for the conditions described above
yield <Az> 9:      The reduction of < A > below that
to be expected from <p2> in the bulk appears well
substantiated.
         To investigate the time dependence of    z
the schlieren system was illuminated using a stro-
boscope. The surface deformation at various phases
of the heating cycle could thus be obsverved. No
change in levelas a function of phase could be
observed although changes of Az of the order of
5 % should have been easily observable,
         We conclude that the amplitude of the time
dependence of the surface deformation must be at
least 20 times smaller than the variation of <z>
with position. Clearly far more sophisticated expe-
                                         4.
riments will be needed to test equation ( )
         This work was supported financially by a
grant from the Swiss National Science Foundation.

				
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